By creating illusions : With Manta Style you get a brief period of invulnerability when you use it, CK's Phantasm will give you 0.5s, Naga Siren's Mirror Image will give you 0.3s.

By Banishing yourself : Lifestealer's infest or Puck's Phase Shift

By Transforming yourself : Abilities that morph your hero grant some tiny frames of invulnerability so if timed well you can transform disjoint with : Chemical Rage (Alchemist), True Form (Lone Druid) and Metamorphosis (Terrorblade)

Becoming invisible will disjoint projectiles but not Assassinate (since Assassinate gives true sight of the target)

By Becoming invulnerable :

Invulnerability is granted by several skills (and Eul's Scepter) in the game. You can become invulnerable by

Being disabled : Using Eul's Scepter on yourself, same goes if you get Nightmared by Bane, Slept by Song onf the Siren, Disrupted (Shadow demon) or Astrast Emprisonned by Outworld Devourer etc (full list on the link).

Being hidden : During Juggernaught Ultimate, or Ember's Sleight of Fist, Lifestealer's
infest or Phoenix's Supernova(full list on the link).

Not sure exactly what you mean, but it will cancel your heal if you're currently using a bottle. If you've almost got enough hp to survive, you may get enough from your bottle. But it should be a general rule that if you have bottle charges and are escaping low health you should use them asap.
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Shane IvoKid ReidMar 5 '14 at 10:27

i mean if am using bottle and sniper's ultimate hit me i get damage ?
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Omer ObaidMar 5 '14 at 10:37

Blink or any disjointing ability. Becoming magic immune in any way works.Primal Split, Supernova, Euls, Astrals emprisonements, and disruption falls under the same category : becoming invulnerable (along with a lot of other spells like nightmare or Song of the Siren). You can dodge by creating illusions with Naga and Chaos Knight aswell.
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WizLizMar 5 '14 at 11:33

I edited your post so it's exhaustive and sorted by category. Hope you dont mind :). I will have to test X marks the spot and glimps because i think it doesnt disjoint
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WizLizMar 7 '14 at 7:58

Sniper's ultimate Assassinate is single target magic damage. Anything that blocks single target spells or makes you immune to magic damage will prevent it and it's damage can be reduced through magic resist such as cloak, hood, or pipe. The projectile, while fast, can be disjointed. Sniper can also be interrupted as it's a channeling ability prior to firing.

The request for specific hero abilities who can avoid it is somewhat unreasonable because there are so many. Look at the heroes you like to play and dig into their abilities. Anything that allows for disjoints (blinks, tornadoes, removals, invulnerabilities, slark's ult) can dodge the in air bullet with timing.

The quick list of items that can help you with the damage is: Hood, Pipe, Linkens, Euls, BKB, TP, Manta, Blink, Bloodstone, and finally if you're losing stack bracers.

The answer with all information you have was already posted 1 day before. Why do you post it again?
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MikroDelMay 30 '14 at 5:56

@MikroDel If you watch carefully, the current accepted answer was not exhaustive and I edited it to make it complete but I edited it after I posted my answer. I figured after posting that editing the currently accepted answer would be more helpful
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WizLizMay 30 '14 at 21:56

Thank you for your response on my comment. After the information you have given - the original answer of "Shane IvoKid Reid" was changed completely with your edits. Its not what the edits should do.
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MikroDelMay 31 '14 at 10:14

@MikroDel Yes i agree but the answer was accepted in a state that I concidered incomplete and wrong for some information. For the sake of the quality of the content of Arqade, I felt it was more right to edit the accepted answer in order make it right and leaving a comment explaiing why i did that. Tell me if you fell that was the right choice or not but for me it was.
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WizLizMay 31 '14 at 19:04